(185t) Multi-Scale Simultaneous Parameter Estimation in Rate-Based Processes

Unbiased and consistent
estimation of model parameters using noisy experimental data is an essential
requirement for developing predictive models. While there has been considerable
progress in this area in the last few decades, optimal estimation of model
parameters is still challenging for reactive solvent-based processes.
Simultaneous mass and heat transfer coupled with fast chemical reactions that
cannot be distinguished from each other make the parameter estimation problem
for these systems considerably more difficult. The typical approach in the
literature to circumvent this problem is to develop these models sequentially
by designing experiments that attempt to isolate a specific mechanism. For
example, a diffusivity model is first developed considering a surrogate system
where no reaction takes place. Then, data from a bench scale wetted wall column
(WWC) is used to develop models for the mass transfer coefficients and reaction
kinetics, where the previously established diffusivity model is assumed to be
valid. Finally, an interfacial area model is developed for a given packing
based on pilot scale absorber and regenerator data. Another approach is to
obtain the mass transfer coefficient model using experimental data from a
nonreactive system in the packed tower. Then data for the actual, reactive
system can be used to develop the interfacial area submodel.

The traditional sequential approach
implicitly assumes that the diffusivity and mass transfer coefficient models
obtained from different types of equipment are valid for each type of equipment
and system (e.g., that the WWC column and non-reactive system are valid for the
reactive system in a packed column). However, the hydrodynamics, liquid and gas
velocities, loading of the solvent and operating temperatures can be very
different. Also, significant differences in density, viscosity, and surface
tension between the reactive and non-reactive systems can affect the
wettability and flow characteristics of the fluids, hence the interfacial area.
Furthermore, the mass transfer for electrolyte systems is affected by the ionic
species present in the solution, ion-molecule interactions, and ion mobility.
Therefore, the parameters that are estimated for a given scale or a surrogate
system may not be necessarily optimal for the system. Thus, the error in
parameter estimation from one step gets propagated to the next step.

In this work, a novel
simultaneous parameter estimation technique is developed where parameters for mass
transfer, diffusivity, interfacial area, and reaction kinetics are optimally estimated
leveraging noisy, experimental data from multiple scales (mm-scale to m-scale)
and operating conditions using high-fidelity process models (Chinen et al.,
2018). The proposed approach leads to a
large-scale optimization problem consisting of a large number of parameters and
millions of linear and nonlinear equality and inequality constraints. The
optimization problem is solved using the Institute for the  Design of Advanced
Energy Systems’ (IDAES) computational framework
that facilitates large-scale parameter estimation at multiple scales embedded
in complex process models and property submodels while
utilizing data from various sources and scales (Eslick et al.,
2018).  The software platform provides modular process modeling capabilities
using the Pyomo algebraic modeling language (Hart
et al., 2011) and the PySP module in Pyomo for stochastic
programming and parameter estimation (Watson
et al., 2012).  Our previous work focused on the parameter
estimation problem for a MEA-H₂O-CO₂ system where the
data from the WWC and pilot plant were used (Eslick
et al., 2018). The Non-random-two-liquid (NRTL) model was implemented to model the vapor-liquid equilibrium at the interface of
the liquid/gas films. Even though the WWC and
packed tower models were rigorous in that work, a simple mass transfer model
was used to describe the CO₂ and H₂O transport across the
liquid and gas films. In particular, it was assumed that the change in the
concentration driving force is linear across the films. Chemical reactions in
the liquid film were not explicitly considered in that model, rather an
enhancement factor was used to capture the enhancement in mass transfer due to
the chemical reactions. However, due to the fast ionic reactions in the liquid
film of the MEA-H₂O-CO₂ system, complex thermodynamics of
this electrolyte system, and interactions between the molecular and ionic
species, the CO₂ concentration profile in the liquid film is highly
nonlinear. Therefore, the parameter estimates under linear assumption can be
inaccurate. In the updated model, simultaneous
mass transfer and chemical reactions are considered in the liquid film. Multicomponent mass transfer in the liquid and gas films is
modeled by the Maxwell-Stefan equations.
Furthermore, a rigorous electrolyte NRTL model is implemented to model the
vapor-liquid equilibrium at the interface of the liquid/gas films. Experimental
data sets are also expanded to include the data from the WWC, bench-scale, and
pilot-scale systems extending the richness of the experimental data
considerably. These modifications increased the size of the optimization
problem substantially. Model reformulations are carried out and novel solution
strategies are developed to solve the parameter estimation problem within
reasonable time.  Various approaches
investigated in this work includes direct simultaneous optimization,
decomposition via PySP and an approach using cross-validation and statistical
inference. It is observed that the variance in the parameter estimates can be
substantially improved by including the data from multi-scale systems
simultaneously.

A. S. Chinen, J. C. Morgan, B.
Omell, D. Bhattacharyya, C. Tong, D. C. Miller, 2018,  Development of a
gold-standard model for solvent-based CO2 capture. Part 1: hydraulic and mass
transfer models and  their uncertainty quantification, (internal review )

J. C. Eslick, P. T. Akula, D.
Bhattacharyya, D. C. Miller, 2018, Simultaneous Parameter Estimation in
Reactive-Solvent-Based Processes, PSE 2018 conference San Diego.

J.-P. Watson, D. L. Woodruff
and W. E. Hart (2012). PySP: modeling and solving stochastic programs in
Python. Mathematical Programming Computation 4(2): 109-149  

W. E. Hart, J.-P. Watson and D. L. Woodruff (2011). Pyomo: modeling
and solving mathematical programs in Python. Mathematical Programming
Computation 3(3): 219-260